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On the Extinction of a Class of Population-Size-Dependent Bisexual Branching Processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Yongsheng Xing  and
Yongjin Wang
Yongsheng Xing*
Affiliation:
Nankai University
Yongjin Wang*
Affiliation:
Nankai University
*
∗Postal address: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China.
∗∗Email address: yjwang@nankai.edu.cn
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Abstract

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In this paper, we study a class of bisexual Galton-Watson branching processes in which the law of offspring distribution is dependent on the population size. Under a suitable condition on the offspring distribution, we prove that the limit of mean growth-rate per mating unit exists. Based on this limit, we give a criterion to identify whether the process admits ultimate extinction with probability one.

Keywords

Bisexual Galton-Watson branching processpopulation-size-dependent branching processextinction probability

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 175 - 184
Copyright
© Applied Probability Trust 2005 

Footnotes

Supported by the Natural Science Foundation of China (grant no. 10131040).

References

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